Probability distributions for locations of calling animals, receivers, sound speeds, winds, and data from travel time differences.
A new nonlinear sequential Monte Carlo technique is used to estimate posterior probability distributions for the location of a calling animal, the locations of acoustic receivers, sound speeds, winds, and the differences in sonic travel time between pairs of receivers from measurements of those differences, while adopting realistic prior distributions of the variables. Other algorithms in the literature appear to be too inefficient to yield distributions for this large number of variables (up to 41) without recourse to a linear approximation. The new technique overcomes the computational inefficiency of other algorithms because it does not sequentially propagate the joint probability distribution of the variables between adjacent data. Instead, the lower and upper bounds of the distributions are propagated. The technique is applied to commonly encountered problems that were previously intractable such as estimating how accurately sound speed and poorly known initial locations of receivers can be estimated from the differences in sonic travel time from calling animals, while explicitly modeling distributions of all the variables in the problem. In both cases, the new technique yields one or two orders of magnitude improvements compared with initial uncertainties. The technique is suitable for accurately estimating receiver locations from animal calls.